Desterrado means "banished" or "exiled." It's a strong and evocative word that isn't commonly found in everyday Spanish songs, making it stand out.
In the context of "Edén," the artist sings, "Mordí la manzana prohibida y ahora del Edén estoy desterrado" (I bit the forbidden apple and now I am banished from Eden). This line directly references the biblical story of Adam and Eve, using the word to convey a profound sense of loss, regret, and separation from a perfect state or relationship.
Nyno Vargas's song "Edén" is a really emotional journey through regret and lost love. He's looking back at a relationship that ended, and he's realizing just how much he messed up. He sings, "Ahora que no te tengo, me he dado cuenta que sin ti me muero" [Now that I don't have you, I've realized that without you I die], which perfectly sums up that feeling of emptiness after a breakup.
He uses the powerful image of being "desterrado del Edén" [banished from Eden] because he "mordí la manzana prohibida" [bit the forbidden apple], which is such a great way to say he made a big mistake that cost him everything. Even though he wants to fix things, his pride is holding him back, as he admits, "el orgullo me tiene atado" [pride has me tied up]. It's a really honest look at how hard it is to move on when you're still stuck on what could have been.